Fredholm-Volterra Integral Equation with Potential Kernel

Abstract

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω) × C(O, T), Ω = {(x, y) \(\in\) Ω : \(\sqrt{{x^2}+{y^2}}\) ≤ a, z = 0} and T < ∞. The kernel of the Fredholm integral term is considered in the generalized potential form belongs to the class C ([Ω] × [Ω]), while the kernel of Volterra integral term is a positive and continuous function belongs to the class C[0,T). Also in this work the solution of Fredholm integral equation of the second and first kind with a potential kernel is discussed. Many interesting cases are derived and established from the wok.